You must do all of the quests in the BAAA machine in order to earn this achievement.
1. Chocolate Factory. You will need to head over by the pirate ship and get a bag of "chocolate" from the vendor. Go across the street, light it on fire, then place it on the nearby doorstep.
2. Drill for Cheese. You will first have to find the security building that the tracker shows you. Go inside through the revolving door (seriously irritating) and find the vault. Then leave and find a drill. Come back, drill the door to find another door. Leave and find another drill and go back and drill this door. Find yet a third door, leave, get a drill, go back and drill the third door. Inside the vault you will find a rocket launcher modifier and a grilled cheese sandwich.
3. Mess with the police. Go to the police station and hop up on the building and knock the doughnut sign down.
4. Cops and robbers. Go to the bank and lick a bank robber. Drag him across the street to the building with a bunch of open doors and drag him into a cell.
5. Flippin Burgs. Go to the hamburger joint. Behind the burger joint you will find a couple of trash cans and a bag of trash. Lick the bag of trash, hop on the roof and drop it into the glowing pipe. Then go inside to the burger you should have seen being made and lick one. Take it to an NPC.
6. Make cops fly. Across from the bank is a hot air balloon. Lick a cop, take him to the hot air balloon. He should automatically be attached to the balloon but you will need to release him with
. There are some buildings right next to you on the same side of the street. Behind the building in an alley of sorts in the back corner are a couple of cannisters. Lick one and drag it to the balloon.
7. Catastrophe. Behind a couple of buildings by the railroad tracks are some shacks. They have signs about how much they love pussy. Lick and drag 3 cats to these shacks. This will unlock a temple in the desert and going in the temple will give you a very annoying cat mod that doesn't seem to go away when you turn it off.
8. Exploding cake. Go the birthday party, which is a couple of doors down from the "chocolate" vendor. When you approach the cake it will show you the location of some dynamite. Fetch the dynamite and return to the cake. Then, back up, following the red wire to the plunger and press
9. Drive in Saturday. Go to the drive in and hop up to the projector and kick, lick, whatever you want to it.
10, Buried games. There is a vault on a hill in between the railroad tracks and the road. Get a drill and drill it twice. Fall down in the hole and lick the disc. The hard part is getting out of the hole. I used the anti gravity mutator and jumped up and out. Go to the pirate ship. On the main deck is a cabin you can go in. After it takes the disc from you the ship will SLOWLY move away. Just stay on the ship until you appear on the moon. If you haven't gotten the moon achievement yet you will get it here.
11. Prison Break: The Dev. Over by where the canisters for the hot air balloon was, there is a Drillicopter. Go pick it up then head to the police station. Lick the dev and then drag him to the golden goat in the casino.
Edit 12/9: As reported by many in comments this can be one of the glitchier missions. You may have to do several things in order to get this one to actually work. This includes, but is not limited to respawning or restarting if the dev disappears or gets stuck somewhere. I retried this and had him get stuck while entering the casino forcing me to go back to the baaa machine and choosing the mission again. Even though I had the drillicopter attached it allowed me to go back and get it again and the dev was back in the jail area. If you are having issues please read the comments for other ideas. Thanks for all that have posted replies.
12. Space Cow. Out by the start area is a fenced in bunch of cows. Lick one then drag them over to the building that you are shown. It is just below the casino so I went to the backside of the casino and jumped over to the building that was needed dragging the cow with me. Set the cow in the middle and it should get sucked up into the space ship.
13. The Godmother. Grab a drill. Go to the casino. Just past the slots inside is a passage that will take you behind the stage to your left of up some stairs to the right. Go up the stairs. In this room is a rotating red beam. If you can make it to your left to another room there is a vault inside. Drill the vault and inside you will find the Godmother.
Your achievement should pop when you have completed all of these quests.